Simplify the following expression: $a = \dfrac{-10z^2 - 80z - 70}{z + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ a =\dfrac{-10(z^2 + 8z + 7)}{z + 7} $ Then we factor the remaining polynomial: $z^2 + {8}z + {7} $ ${7} + {1} = {8}$ ${7} \times {1} = {7}$ $ (z + {7}) (z + {1}) $ This gives us a factored expression: $\dfrac{-10(z + {7}) (z + {1})}{z + 7}$ We can divide the numerator and denominator by $(z - 7)$ on condition that $z \neq -7$ Therefore $a = -10(z + 1); z \neq -7$